Origin of the Growing Length Scale in M-p-Spin Glass Models

TL;DR

This study uses renormalization group analysis on M-p-spin glass models to investigate the origin of the growing length scale, challenging the random first order transition theory and suggesting an analogy with Ising spin glasses in a field.

Contribution

It provides a detailed analysis of two M-p-spin models, revealing that the growing length scale is not due to RFOT mechanisms but resembles spin glass behavior in a field.

Findings

Both models show similar behavior across dimensions.

The length scale growth is not due to RFOT but akin to spin glasses in a field.

Models exhibit Gardner transition and glass-like states.

Abstract

Two versions of the M-p-spin glass model have been studied with the Migdal-Kadanoff renormalization group approximation. The model with p=3 and M=3 has at mean-field level the ideal glass transition at the Kauzmann temperature and at lower temperatures still the Gardner transition to a state like that of an Ising spin glass in a field. The model with p=3 and M=2 has only the Gardner transition. In the dimensions studied, d=2,3 and 4, both models behave almost identically, indicating that the growing correlation length as the temperature is reduced in these models -- the analogue of the point-to-set length scale -- is not due to the mechanism postulated in the random first order transition theory of glasses, but is more like that expected on the analogy of glasses to the Ising spin glass in a field.